YES
Time: 0.308

Problem:
 Equations:
  plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
  plusAC(x3,x4) -> plusAC(x4,x3)
  timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
  timesAC(x3,x4) -> timesAC(x4,x3)
  plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
  plusAC(x4,x3) -> plusAC(x3,x4)
  timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
  timesAC(x4,x3) -> timesAC(x3,x4)
 TRS:
  plusAC(x,0()) -> x
  plusAC(0(),y) -> y
  plusAC(s(x),y) -> s(plusAC(x,y))
  timesAC(0(),y) -> 0()
  timesAC(s(0()),y) -> y
  timesAC(s(x),y) -> plusAC(y,timesAC(x,y))
  div(0(),y) -> 0()
  div(x,y) -> quot(x,y,y)
  quot(0(),s(y),z) -> 0()
  quot(s(x),s(y),z) -> quot(x,y,z)
  quot(x,0(),s(z)) -> s(div(x,s(z)))
  div(div(x,y),z) -> div(x,timesAC(y,z))

Proof:
 DP Processor:
  Equations#:
   plus{AC,#}(plusAC(x3,x4),x5) -> plus{AC,#}(x3,plusAC(x4,x5))
   plus{AC,#}(x3,x4) -> plus{AC,#}(x4,x3)
   times{AC,#}(timesAC(x3,x4),x5) -> times{AC,#}(x3,timesAC(x4,x5))
   times{AC,#}(x3,x4) -> times{AC,#}(x4,x3)
   plus{AC,#}(x3,plusAC(x4,x5)) -> plus{AC,#}(plusAC(x3,x4),x5)
   plus{AC,#}(x4,x3) -> plus{AC,#}(x3,x4)
   times{AC,#}(x3,timesAC(x4,x5)) -> times{AC,#}(timesAC(x3,x4),x5)
   times{AC,#}(x4,x3) -> times{AC,#}(x3,x4)
  DPs:
   plus{AC,#}(s(x),y) -> plus{AC,#}(x,y)
   times{AC,#}(s(x),y) -> times{AC,#}(x,y)
   times{AC,#}(s(x),y) -> plus{AC,#}(y,timesAC(x,y))
   div#(x,y) -> quot#(x,y,y)
   quot#(s(x),s(y),z) -> quot#(x,y,z)
   quot#(x,0(),s(z)) -> div#(x,s(z))
   div#(div(x,y),z) -> times{AC,#}(y,z)
   div#(div(x,y),z) -> div#(x,timesAC(y,z))
   plus{AC,#}(x6,plusAC(x,0())) -> plus{AC,#}(x6,x)
   plus{AC,#}(x7,plusAC(0(),y)) -> plus{AC,#}(x7,y)
   plus{AC,#}(x8,plusAC(s(x),y)) -> plus{AC,#}(x,y)
   plus{AC,#}(x8,plusAC(s(x),y)) -> plus{AC,#}(x8,s(plusAC(x,y)))
   times{AC,#}(x9,timesAC(0(),y)) -> times{AC,#}(x9,0())
   times{AC,#}(x10,timesAC(s(0()),y)) -> times{AC,#}(x10,y)
   times{AC,#}(x11,timesAC(s(x),y)) -> times{AC,#}(x,y)
   times{AC,#}(x11,timesAC(s(x),y)) -> plus{AC,#}(y,timesAC(x,y))
   times{AC,#}(x11,timesAC(s(x),y)) -> times{AC,#}(x11,plusAC(y,timesAC(x,y)))
  Equations:
   plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
   plusAC(x3,x4) -> plusAC(x4,x3)
   timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
   timesAC(x3,x4) -> timesAC(x4,x3)
   plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
   plusAC(x4,x3) -> plusAC(x3,x4)
   timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
   timesAC(x4,x3) -> timesAC(x3,x4)
  TRS:
   plusAC(x,0()) -> x
   plusAC(0(),y) -> y
   plusAC(s(x),y) -> s(plusAC(x,y))
   timesAC(0(),y) -> 0()
   timesAC(s(0()),y) -> y
   timesAC(s(x),y) -> plusAC(y,timesAC(x,y))
   div(0(),y) -> 0()
   div(x,y) -> quot(x,y,y)
   quot(0(),s(y),z) -> 0()
   quot(s(x),s(y),z) -> quot(x,y,z)
   quot(x,0(),s(z)) -> s(div(x,s(z)))
   div(div(x,y),z) -> div(x,timesAC(y,z))
  S:
   plus{AC,#}(plusAC(x12,x13),x14) -> plus{AC,#}(x12,x13)
   plus{AC,#}(x12,plusAC(x13,x14)) -> plus{AC,#}(x13,x14)
   times{AC,#}(timesAC(x12,x13),x14) -> times{AC,#}(x12,x13)
   times{AC,#}(x12,timesAC(x13,x14)) -> times{AC,#}(x13,x14)
  AC-EDG Processor:
   Equations#:
    plus{AC,#}(plusAC(x3,x4),x5) -> plus{AC,#}(x3,plusAC(x4,x5))
    plus{AC,#}(x3,x4) -> plus{AC,#}(x4,x3)
    times{AC,#}(timesAC(x3,x4),x5) -> times{AC,#}(x3,timesAC(x4,x5))
    times{AC,#}(x3,x4) -> times{AC,#}(x4,x3)
    plus{AC,#}(x3,plusAC(x4,x5)) -> plus{AC,#}(plusAC(x3,x4),x5)
    plus{AC,#}(x4,x3) -> plus{AC,#}(x3,x4)
    times{AC,#}(x3,timesAC(x4,x5)) -> times{AC,#}(timesAC(x3,x4),x5)
    times{AC,#}(x4,x3) -> times{AC,#}(x3,x4)
   DPs:
    plus{AC,#}(s(x),y) -> plus{AC,#}(x,y)
    times{AC,#}(s(x),y) -> times{AC,#}(x,y)
    times{AC,#}(s(x),y) -> plus{AC,#}(y,timesAC(x,y))
    div#(x,y) -> quot#(x,y,y)
    quot#(s(x),s(y),z) -> quot#(x,y,z)
    quot#(x,0(),s(z)) -> div#(x,s(z))
    div#(div(x,y),z) -> times{AC,#}(y,z)
    div#(div(x,y),z) -> div#(x,timesAC(y,z))
    plus{AC,#}(x6,plusAC(x,0())) -> plus{AC,#}(x6,x)
    plus{AC,#}(x7,plusAC(0(),y)) -> plus{AC,#}(x7,y)
    plus{AC,#}(x8,plusAC(s(x),y)) -> plus{AC,#}(x,y)
    plus{AC,#}(x8,plusAC(s(x),y)) -> plus{AC,#}(x8,s(plusAC(x,y)))
    times{AC,#}(x9,timesAC(0(),y)) -> times{AC,#}(x9,0())
    times{AC,#}(x10,timesAC(s(0()),y)) -> times{AC,#}(x10,y)
    times{AC,#}(x11,timesAC(s(x),y)) -> times{AC,#}(x,y)
    times{AC,#}(x11,timesAC(s(x),y)) -> plus{AC,#}(y,timesAC(x,y))
    times{AC,#}(x11,timesAC(s(x),y)) -> times{AC,#}(x11,plusAC(y,timesAC(x,y)))
   Equations:
    plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
    plusAC(x3,x4) -> plusAC(x4,x3)
    timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
    timesAC(x3,x4) -> timesAC(x4,x3)
    plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
    plusAC(x4,x3) -> plusAC(x3,x4)
    timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
    timesAC(x4,x3) -> timesAC(x3,x4)
   TRS:
    plusAC(x,0()) -> x
    plusAC(0(),y) -> y
    plusAC(s(x),y) -> s(plusAC(x,y))
    timesAC(0(),y) -> 0()
    timesAC(s(0()),y) -> y
    timesAC(s(x),y) -> plusAC(y,timesAC(x,y))
    div(0(),y) -> 0()
    div(x,y) -> quot(x,y,y)
    quot(0(),s(y),z) -> 0()
    quot(s(x),s(y),z) -> quot(x,y,z)
    quot(x,0(),s(z)) -> s(div(x,s(z)))
    div(div(x,y),z) -> div(x,timesAC(y,z))
   S:
    plus{AC,#}(plusAC(x12,x13),x14) -> plus{AC,#}(x12,x13)
    plus{AC,#}(x12,plusAC(x13,x14)) -> plus{AC,#}(x13,x14)
    times{AC,#}(timesAC(x12,x13),x14) -> times{AC,#}(x12,x13)
    times{AC,#}(x12,timesAC(x13,x14)) -> times{AC,#}(x13,x14)
   SCC Processor:
    #sccs: 3
    #rules: 14
    #arcs: 87/289
    Equations#:
     plus{AC,#}(plusAC(x3,x4),x5) -> plus{AC,#}(x3,plusAC(x4,x5))
     plus{AC,#}(x3,x4) -> plus{AC,#}(x4,x3)
     times{AC,#}(timesAC(x3,x4),x5) -> times{AC,#}(x3,timesAC(x4,x5))
     times{AC,#}(x3,x4) -> times{AC,#}(x4,x3)
     plus{AC,#}(x3,plusAC(x4,x5)) -> plus{AC,#}(plusAC(x3,x4),x5)
     plus{AC,#}(x4,x3) -> plus{AC,#}(x3,x4)
     times{AC,#}(x3,timesAC(x4,x5)) -> times{AC,#}(timesAC(x3,x4),x5)
     times{AC,#}(x4,x3) -> times{AC,#}(x3,x4)
    DPs:
     quot#(s(x),s(y),z) -> quot#(x,y,z)
     quot#(x,0(),s(z)) -> div#(x,s(z))
     div#(div(x,y),z) -> div#(x,timesAC(y,z))
     div#(x,y) -> quot#(x,y,y)
    Equations:
     plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
     plusAC(x3,x4) -> plusAC(x4,x3)
     timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
     timesAC(x3,x4) -> timesAC(x4,x3)
     plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
     plusAC(x4,x3) -> plusAC(x3,x4)
     timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
     timesAC(x4,x3) -> timesAC(x3,x4)
    TRS:
     plusAC(x,0()) -> x
     plusAC(0(),y) -> y
     plusAC(s(x),y) -> s(plusAC(x,y))
     timesAC(0(),y) -> 0()
     timesAC(s(0()),y) -> y
     timesAC(s(x),y) -> plusAC(y,timesAC(x,y))
     div(0(),y) -> 0()
     div(x,y) -> quot(x,y,y)
     quot(0(),s(y),z) -> 0()
     quot(s(x),s(y),z) -> quot(x,y,z)
     quot(x,0(),s(z)) -> s(div(x,s(z)))
     div(div(x,y),z) -> div(x,timesAC(y,z))
    S:
     plus{AC,#}(plusAC(x12,x13),x14) -> plus{AC,#}(x12,x13)
     plus{AC,#}(x12,plusAC(x13,x14)) -> plus{AC,#}(x13,x14)
     times{AC,#}(timesAC(x12,x13),x14) -> times{AC,#}(x12,x13)
     times{AC,#}(x12,timesAC(x13,x14)) -> times{AC,#}(x13,x14)
    AC-DP unlabeling:
     Equations#:
      plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
      plusAC(x3,x4) -> plusAC(x4,x3)
      timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
      timesAC(x3,x4) -> timesAC(x4,x3)
      plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
      plusAC(x4,x3) -> plusAC(x3,x4)
      timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
      timesAC(x4,x3) -> timesAC(x3,x4)
     DPs:
      quot#(s(x),s(y),z) -> quot#(x,y,z)
      quot#(x,0(),s(z)) -> div#(x,s(z))
      div#(div(x,y),z) -> div#(x,timesAC(y,z))
      div#(x,y) -> quot#(x,y,y)
     Equations:
      plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
      plusAC(x3,x4) -> plusAC(x4,x3)
      timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
      timesAC(x3,x4) -> timesAC(x4,x3)
      plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
      plusAC(x4,x3) -> plusAC(x3,x4)
      timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
      timesAC(x4,x3) -> timesAC(x3,x4)
     TRS:
      plusAC(x,0()) -> x
      plusAC(0(),y) -> y
      plusAC(s(x),y) -> s(plusAC(x,y))
      timesAC(0(),y) -> 0()
      timesAC(s(0()),y) -> y
      timesAC(s(x),y) -> plusAC(y,timesAC(x,y))
      div(0(),y) -> 0()
      div(x,y) -> quot(x,y,y)
      quot(0(),s(y),z) -> 0()
      quot(s(x),s(y),z) -> quot(x,y,z)
      quot(x,0(),s(z)) -> s(div(x,s(z)))
      div(div(x,y),z) -> div(x,timesAC(y,z))
     S:
      plusAC(plusAC(x12,x13),x14) -> plusAC(x12,x13)
      plusAC(x12,plusAC(x13,x14)) -> plusAC(x13,x14)
      timesAC(timesAC(x12,x13),x14) -> timesAC(x12,x13)
      timesAC(x12,timesAC(x13,x14)) -> timesAC(x13,x14)
     Usable Rule Processor:
      Equations#:
       plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
       plusAC(x3,x4) -> plusAC(x4,x3)
       timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
       timesAC(x3,x4) -> timesAC(x4,x3)
       plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
       plusAC(x4,x3) -> plusAC(x3,x4)
       timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
       timesAC(x4,x3) -> timesAC(x3,x4)
      DPs:
       quot#(s(x),s(y),z) -> quot#(x,y,z)
       quot#(x,0(),s(z)) -> div#(x,s(z))
       div#(div(x,y),z) -> div#(x,timesAC(y,z))
       div#(x,y) -> quot#(x,y,y)
      Equations:
       plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
       plusAC(x3,x4) -> plusAC(x4,x3)
       timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
       timesAC(x3,x4) -> timesAC(x4,x3)
       plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
       plusAC(x4,x3) -> plusAC(x3,x4)
       timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
       timesAC(x4,x3) -> timesAC(x3,x4)
      TRS:
       timesAC(0(),y) -> 0()
       timesAC(s(0()),y) -> y
       timesAC(s(x),y) -> plusAC(y,timesAC(x,y))
       plusAC(x,0()) -> x
       plusAC(0(),y) -> y
       plusAC(s(x),y) -> s(plusAC(x,y))
      S:
       plusAC(plusAC(x12,x13),x14) -> plusAC(x12,x13)
       plusAC(x12,plusAC(x13,x14)) -> plusAC(x13,x14)
       timesAC(timesAC(x12,x13),x14) -> timesAC(x12,x13)
       timesAC(x12,timesAC(x13,x14)) -> timesAC(x13,x14)
      AC-RPO Processor:
       argument filtering:
        pi(plusAC) = []
        pi(timesAC) = [0,1]
        pi(0) = []
        pi(s) = [0]
        pi(div) = 0
        pi(div#) = 0
        pi(quot#) = 0
       precedence:
        s > quot# > div > timesAC > 0 > div# > plusAC
       status:
        quot#:mul  div#:mul  div:mul  
       problem:
        Equations#:
         plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
         plusAC(x3,x4) -> plusAC(x4,x3)
         timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
         timesAC(x3,x4) -> timesAC(x4,x3)
         plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
         plusAC(x4,x3) -> plusAC(x3,x4)
         timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
         timesAC(x4,x3) -> timesAC(x3,x4)
        DPs:
         quot#(x,0(),s(z)) -> div#(x,s(z))
         div#(div(x,y),z) -> div#(x,timesAC(y,z))
         div#(x,y) -> quot#(x,y,y)
        Equations:
         plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
         plusAC(x3,x4) -> plusAC(x4,x3)
         timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
         timesAC(x3,x4) -> timesAC(x4,x3)
         plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
         plusAC(x4,x3) -> plusAC(x3,x4)
         timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
         timesAC(x4,x3) -> timesAC(x3,x4)
        TRS:
         timesAC(0(),y) -> 0()
         timesAC(s(0()),y) -> y
         timesAC(s(x),y) -> plusAC(y,timesAC(x,y))
         plusAC(x,0()) -> x
         plusAC(0(),y) -> y
         plusAC(s(x),y) -> s(plusAC(x,y))
        S:
         plusAC(plusAC(x12,x13),x14) -> plusAC(x12,x13)
         plusAC(x12,plusAC(x13,x14)) -> plusAC(x13,x14)
         timesAC(timesAC(x12,x13),x14) -> timesAC(x12,x13)
         timesAC(x12,timesAC(x13,x14)) -> timesAC(x13,x14)
       Restore Modifier:
        Equations#:
         plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
         plusAC(x3,x4) -> plusAC(x4,x3)
         timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
         timesAC(x3,x4) -> timesAC(x4,x3)
         plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
         plusAC(x4,x3) -> plusAC(x3,x4)
         timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
         timesAC(x4,x3) -> timesAC(x3,x4)
        DPs:
         quot#(x,0(),s(z)) -> div#(x,s(z))
         div#(div(x,y),z) -> div#(x,timesAC(y,z))
         div#(x,y) -> quot#(x,y,y)
        Equations:
         plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
         plusAC(x3,x4) -> plusAC(x4,x3)
         timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
         timesAC(x3,x4) -> timesAC(x4,x3)
         plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
         plusAC(x4,x3) -> plusAC(x3,x4)
         timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
         timesAC(x4,x3) -> timesAC(x3,x4)
        TRS:
         timesAC(0(),y) -> 0()
         timesAC(s(0()),y) -> y
         timesAC(s(x),y) -> plusAC(y,timesAC(x,y))
         plusAC(x,0()) -> x
         plusAC(0(),y) -> y
         plusAC(s(x),y) -> s(plusAC(x,y))
        S:
         plusAC(plusAC(x12,x13),x14) -> plusAC(x12,x13)
         plusAC(x12,plusAC(x13,x14)) -> plusAC(x13,x14)
         timesAC(timesAC(x12,x13),x14) -> timesAC(x12,x13)
         timesAC(x12,timesAC(x13,x14)) -> timesAC(x13,x14)
        AC-DP unlabeling:
         Equations#:
          plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
          plusAC(x3,x4) -> plusAC(x4,x3)
          timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
          timesAC(x3,x4) -> timesAC(x4,x3)
          plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
          plusAC(x4,x3) -> plusAC(x3,x4)
          timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
          timesAC(x4,x3) -> timesAC(x3,x4)
         DPs:
          quot#(x,0(),s(z)) -> div#(x,s(z))
          div#(div(x,y),z) -> div#(x,timesAC(y,z))
          div#(x,y) -> quot#(x,y,y)
         Equations:
          plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
          plusAC(x3,x4) -> plusAC(x4,x3)
          timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
          timesAC(x3,x4) -> timesAC(x4,x3)
          plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
          plusAC(x4,x3) -> plusAC(x3,x4)
          timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
          timesAC(x4,x3) -> timesAC(x3,x4)
         TRS:
          timesAC(0(),y) -> 0()
          timesAC(s(0()),y) -> y
          timesAC(s(x),y) -> plusAC(y,timesAC(x,y))
          plusAC(x,0()) -> x
          plusAC(0(),y) -> y
          plusAC(s(x),y) -> s(plusAC(x,y))
         S:
          plusAC(plusAC(x12,x13),x14) -> plusAC(x12,x13)
          plusAC(x12,plusAC(x13,x14)) -> plusAC(x13,x14)
          timesAC(timesAC(x12,x13),x14) -> timesAC(x12,x13)
          timesAC(x12,timesAC(x13,x14)) -> timesAC(x13,x14)
         AC-RPO Processor:
          argument filtering:
           pi(plusAC) = [0,1]
           pi(timesAC) = [0,1]
           pi(0) = []
           pi(s) = []
           pi(div) = [0]
           pi(div#) = 0
           pi(quot#) = 0
          precedence:
           quot# > div > s > timesAC > plusAC > 0 > div#
          status:
           quot#:mul  div#:mul  div:mul  
          problem:
           Equations#:
            plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
            plusAC(x3,x4) -> plusAC(x4,x3)
            timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
            timesAC(x3,x4) -> timesAC(x4,x3)
            plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
            plusAC(x4,x3) -> plusAC(x3,x4)
            timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
            timesAC(x4,x3) -> timesAC(x3,x4)
           DPs:
            quot#(x,0(),s(z)) -> div#(x,s(z))
            div#(x,y) -> quot#(x,y,y)
           Equations:
            plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
            plusAC(x3,x4) -> plusAC(x4,x3)
            timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
            timesAC(x3,x4) -> timesAC(x4,x3)
            plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
            plusAC(x4,x3) -> plusAC(x3,x4)
            timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
            timesAC(x4,x3) -> timesAC(x3,x4)
           TRS:
            timesAC(0(),y) -> 0()
            timesAC(s(0()),y) -> y
            timesAC(s(x),y) -> plusAC(y,timesAC(x,y))
            plusAC(x,0()) -> x
            plusAC(0(),y) -> y
            plusAC(s(x),y) -> s(plusAC(x,y))
           S:
            plusAC(plusAC(x12,x13),x14) -> plusAC(x12,x13)
            plusAC(x12,plusAC(x13,x14)) -> plusAC(x13,x14)
            timesAC(timesAC(x12,x13),x14) -> timesAC(x12,x13)
            timesAC(x12,timesAC(x13,x14)) -> timesAC(x13,x14)
          Restore Modifier:
           Equations#:
            plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
            plusAC(x3,x4) -> plusAC(x4,x3)
            timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
            timesAC(x3,x4) -> timesAC(x4,x3)
            plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
            plusAC(x4,x3) -> plusAC(x3,x4)
            timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
            timesAC(x4,x3) -> timesAC(x3,x4)
           DPs:
            quot#(x,0(),s(z)) -> div#(x,s(z))
            div#(x,y) -> quot#(x,y,y)
           Equations:
            plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
            plusAC(x3,x4) -> plusAC(x4,x3)
            timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
            timesAC(x3,x4) -> timesAC(x4,x3)
            plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
            plusAC(x4,x3) -> plusAC(x3,x4)
            timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
            timesAC(x4,x3) -> timesAC(x3,x4)
           TRS:
            timesAC(0(),y) -> 0()
            timesAC(s(0()),y) -> y
            timesAC(s(x),y) -> plusAC(y,timesAC(x,y))
            plusAC(x,0()) -> x
            plusAC(0(),y) -> y
            plusAC(s(x),y) -> s(plusAC(x,y))
           S:
            plusAC(plusAC(x12,x13),x14) -> plusAC(x12,x13)
            plusAC(x12,plusAC(x13,x14)) -> plusAC(x13,x14)
            timesAC(timesAC(x12,x13),x14) -> timesAC(x12,x13)
            timesAC(x12,timesAC(x13,x14)) -> timesAC(x13,x14)
           AC-DP unlabeling:
            Equations#:
             plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
             plusAC(x3,x4) -> plusAC(x4,x3)
             timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
             timesAC(x3,x4) -> timesAC(x4,x3)
             plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
             plusAC(x4,x3) -> plusAC(x3,x4)
             timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
             timesAC(x4,x3) -> timesAC(x3,x4)
            DPs:
             quot#(x,0(),s(z)) -> div#(x,s(z))
             div#(x,y) -> quot#(x,y,y)
            Equations:
             plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
             plusAC(x3,x4) -> plusAC(x4,x3)
             timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
             timesAC(x3,x4) -> timesAC(x4,x3)
             plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
             plusAC(x4,x3) -> plusAC(x3,x4)
             timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
             timesAC(x4,x3) -> timesAC(x3,x4)
            TRS:
             timesAC(0(),y) -> 0()
             timesAC(s(0()),y) -> y
             timesAC(s(x),y) -> plusAC(y,timesAC(x,y))
             plusAC(x,0()) -> x
             plusAC(0(),y) -> y
             plusAC(s(x),y) -> s(plusAC(x,y))
            S:
             plusAC(plusAC(x12,x13),x14) -> plusAC(x12,x13)
             plusAC(x12,plusAC(x13,x14)) -> plusAC(x13,x14)
             timesAC(timesAC(x12,x13),x14) -> timesAC(x12,x13)
             timesAC(x12,timesAC(x13,x14)) -> timesAC(x13,x14)
            Usable Rule Processor:
             Equations#:
              plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
              plusAC(x3,x4) -> plusAC(x4,x3)
              timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
              timesAC(x3,x4) -> timesAC(x4,x3)
              plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
              plusAC(x4,x3) -> plusAC(x3,x4)
              timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
              timesAC(x4,x3) -> timesAC(x3,x4)
             DPs:
              quot#(x,0(),s(z)) -> div#(x,s(z))
              div#(x,y) -> quot#(x,y,y)
             Equations:
              plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
              plusAC(x3,x4) -> plusAC(x4,x3)
              timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
              timesAC(x3,x4) -> timesAC(x4,x3)
              plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
              plusAC(x4,x3) -> plusAC(x3,x4)
              timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
              timesAC(x4,x3) -> timesAC(x3,x4)
             TRS:
              
             S:
              plusAC(plusAC(x12,x13),x14) -> plusAC(x12,x13)
              plusAC(x12,plusAC(x13,x14)) -> plusAC(x13,x14)
              timesAC(timesAC(x12,x13),x14) -> timesAC(x12,x13)
              timesAC(x12,timesAC(x13,x14)) -> timesAC(x13,x14)
             AC-RPO Processor:
              argument filtering:
               pi(plusAC) = []
               pi(timesAC) = []
               pi(0) = []
               pi(s) = []
               pi(div#) = [1]
               pi(quot#) = 1
              precedence:
               0 > div# > quot# > s > timesAC > plusAC
              status:
               quot#:mul  div#:mul  
              problem:
               Equations#:
                plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
                plusAC(x3,x4) -> plusAC(x4,x3)
                timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
                timesAC(x3,x4) -> timesAC(x4,x3)
                plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
                plusAC(x4,x3) -> plusAC(x3,x4)
                timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
                timesAC(x4,x3) -> timesAC(x3,x4)
               DPs:
                
               Equations:
                plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
                plusAC(x3,x4) -> plusAC(x4,x3)
                timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
                timesAC(x3,x4) -> timesAC(x4,x3)
                plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
                plusAC(x4,x3) -> plusAC(x3,x4)
                timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
                timesAC(x4,x3) -> timesAC(x3,x4)
               TRS:
                
               S:
                plusAC(plusAC(x12,x13),x14) -> plusAC(x12,x13)
                plusAC(x12,plusAC(x13,x14)) -> plusAC(x13,x14)
                timesAC(timesAC(x12,x13),x14) -> timesAC(x12,x13)
                timesAC(x12,timesAC(x13,x14)) -> timesAC(x13,x14)
              Qed
   
   Equations#:
    plus{AC,#}(plusAC(x3,x4),x5) -> plus{AC,#}(x3,plusAC(x4,x5))
    plus{AC,#}(x3,x4) -> plus{AC,#}(x4,x3)
    times{AC,#}(timesAC(x3,x4),x5) -> times{AC,#}(x3,timesAC(x4,x5))
    times{AC,#}(x3,x4) -> times{AC,#}(x4,x3)
    plus{AC,#}(x3,plusAC(x4,x5)) -> plus{AC,#}(plusAC(x3,x4),x5)
    plus{AC,#}(x4,x3) -> plus{AC,#}(x3,x4)
    times{AC,#}(x3,timesAC(x4,x5)) -> times{AC,#}(timesAC(x3,x4),x5)
    times{AC,#}(x4,x3) -> times{AC,#}(x3,x4)
   DPs:
    times{AC,#}(x11,timesAC(s(x),y)) -> times{AC,#}(x11,plusAC(y,timesAC(x,y)))
    times{AC,#}(x11,timesAC(s(x),y)) -> times{AC,#}(x,y)
    times{AC,#}(x10,timesAC(s(0()),y)) -> times{AC,#}(x10,y)
    times{AC,#}(x9,timesAC(0(),y)) -> times{AC,#}(x9,0())
    times{AC,#}(s(x),y) -> times{AC,#}(x,y)
   Equations:
    plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
    plusAC(x3,x4) -> plusAC(x4,x3)
    timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
    timesAC(x3,x4) -> timesAC(x4,x3)
    plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
    plusAC(x4,x3) -> plusAC(x3,x4)
    timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
    timesAC(x4,x3) -> timesAC(x3,x4)
   TRS:
    plusAC(x,0()) -> x
    plusAC(0(),y) -> y
    plusAC(s(x),y) -> s(plusAC(x,y))
    timesAC(0(),y) -> 0()
    timesAC(s(0()),y) -> y
    timesAC(s(x),y) -> plusAC(y,timesAC(x,y))
    div(0(),y) -> 0()
    div(x,y) -> quot(x,y,y)
    quot(0(),s(y),z) -> 0()
    quot(s(x),s(y),z) -> quot(x,y,z)
    quot(x,0(),s(z)) -> s(div(x,s(z)))
    div(div(x,y),z) -> div(x,timesAC(y,z))
   S:
    plus{AC,#}(plusAC(x12,x13),x14) -> plus{AC,#}(x12,x13)
    plus{AC,#}(x12,plusAC(x13,x14)) -> plus{AC,#}(x13,x14)
    times{AC,#}(timesAC(x12,x13),x14) -> times{AC,#}(x12,x13)
    times{AC,#}(x12,timesAC(x13,x14)) -> times{AC,#}(x13,x14)
   AC-DP unlabeling:
    Equations#:
     plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
     plusAC(x3,x4) -> plusAC(x4,x3)
     timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
     timesAC(x3,x4) -> timesAC(x4,x3)
     plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
     plusAC(x4,x3) -> plusAC(x3,x4)
     timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
     timesAC(x4,x3) -> timesAC(x3,x4)
    DPs:
     timesAC(x11,timesAC(s(x),y)) -> timesAC(x11,plusAC(y,timesAC(x,y)))
     timesAC(x11,timesAC(s(x),y)) -> timesAC(x,y)
     timesAC(x10,timesAC(s(0()),y)) -> timesAC(x10,y)
     timesAC(x9,timesAC(0(),y)) -> timesAC(x9,0())
     timesAC(s(x),y) -> timesAC(x,y)
    Equations:
     plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
     plusAC(x3,x4) -> plusAC(x4,x3)
     timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
     timesAC(x3,x4) -> timesAC(x4,x3)
     plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
     plusAC(x4,x3) -> plusAC(x3,x4)
     timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
     timesAC(x4,x3) -> timesAC(x3,x4)
    TRS:
     plusAC(x,0()) -> x
     plusAC(0(),y) -> y
     plusAC(s(x),y) -> s(plusAC(x,y))
     timesAC(0(),y) -> 0()
     timesAC(s(0()),y) -> y
     timesAC(s(x),y) -> plusAC(y,timesAC(x,y))
     div(0(),y) -> 0()
     div(x,y) -> quot(x,y,y)
     quot(0(),s(y),z) -> 0()
     quot(s(x),s(y),z) -> quot(x,y,z)
     quot(x,0(),s(z)) -> s(div(x,s(z)))
     div(div(x,y),z) -> div(x,timesAC(y,z))
    S:
     plusAC(plusAC(x12,x13),x14) -> plusAC(x12,x13)
     plusAC(x12,plusAC(x13,x14)) -> plusAC(x13,x14)
     timesAC(timesAC(x12,x13),x14) -> timesAC(x12,x13)
     timesAC(x12,timesAC(x13,x14)) -> timesAC(x13,x14)
    Usable Rule Processor:
     Equations#:
      plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
      plusAC(x3,x4) -> plusAC(x4,x3)
      timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
      timesAC(x3,x4) -> timesAC(x4,x3)
      plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
      plusAC(x4,x3) -> plusAC(x3,x4)
      timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
      timesAC(x4,x3) -> timesAC(x3,x4)
     DPs:
      timesAC(x11,timesAC(s(x),y)) -> timesAC(x11,plusAC(y,timesAC(x,y)))
      timesAC(x11,timesAC(s(x),y)) -> timesAC(x,y)
      timesAC(x10,timesAC(s(0()),y)) -> timesAC(x10,y)
      timesAC(x9,timesAC(0(),y)) -> timesAC(x9,0())
      timesAC(s(x),y) -> timesAC(x,y)
     Equations:
      plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
      plusAC(x3,x4) -> plusAC(x4,x3)
      timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
      timesAC(x3,x4) -> timesAC(x4,x3)
      plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
      plusAC(x4,x3) -> plusAC(x3,x4)
      timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
      timesAC(x4,x3) -> timesAC(x3,x4)
     TRS:
      timesAC(0(),y) -> 0()
      timesAC(s(0()),y) -> y
      timesAC(s(x),y) -> plusAC(y,timesAC(x,y))
      plusAC(x,0()) -> x
      plusAC(0(),y) -> y
      plusAC(s(x),y) -> s(plusAC(x,y))
     S:
      plusAC(plusAC(x12,x13),x14) -> plusAC(x12,x13)
      plusAC(x12,plusAC(x13,x14)) -> plusAC(x13,x14)
      timesAC(timesAC(x12,x13),x14) -> timesAC(x12,x13)
      timesAC(x12,timesAC(x13,x14)) -> timesAC(x13,x14)
     AC-RPO Processor:
      argument filtering:
       pi(plusAC) = [0,1]
       pi(timesAC) = [0,1]
       pi(0) = []
       pi(s) = []
      precedence:
       timesAC > plusAC > s > 0
      status:
       
      problem:
       Equations#:
        plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
        plusAC(x3,x4) -> plusAC(x4,x3)
        timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
        timesAC(x3,x4) -> timesAC(x4,x3)
        plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
        plusAC(x4,x3) -> plusAC(x3,x4)
        timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
        timesAC(x4,x3) -> timesAC(x3,x4)
       DPs:
        
       Equations:
        plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
        plusAC(x3,x4) -> plusAC(x4,x3)
        timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
        timesAC(x3,x4) -> timesAC(x4,x3)
        plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
        plusAC(x4,x3) -> plusAC(x3,x4)
        timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
        timesAC(x4,x3) -> timesAC(x3,x4)
       TRS:
        timesAC(0(),y) -> 0()
        timesAC(s(0()),y) -> y
        timesAC(s(x),y) -> plusAC(y,timesAC(x,y))
        plusAC(x,0()) -> x
        plusAC(0(),y) -> y
        plusAC(s(x),y) -> s(plusAC(x,y))
       S:
        plusAC(plusAC(x12,x13),x14) -> plusAC(x12,x13)
        plusAC(x12,plusAC(x13,x14)) -> plusAC(x13,x14)
        timesAC(timesAC(x12,x13),x14) -> timesAC(x12,x13)
        timesAC(x12,timesAC(x13,x14)) -> timesAC(x13,x14)
      Qed
   
   Equations#:
    plus{AC,#}(plusAC(x3,x4),x5) -> plus{AC,#}(x3,plusAC(x4,x5))
    plus{AC,#}(x3,x4) -> plus{AC,#}(x4,x3)
    times{AC,#}(timesAC(x3,x4),x5) -> times{AC,#}(x3,timesAC(x4,x5))
    times{AC,#}(x3,x4) -> times{AC,#}(x4,x3)
    plus{AC,#}(x3,plusAC(x4,x5)) -> plus{AC,#}(plusAC(x3,x4),x5)
    plus{AC,#}(x4,x3) -> plus{AC,#}(x3,x4)
    times{AC,#}(x3,timesAC(x4,x5)) -> times{AC,#}(timesAC(x3,x4),x5)
    times{AC,#}(x4,x3) -> times{AC,#}(x3,x4)
   DPs:
    plus{AC,#}(x8,plusAC(s(x),y)) -> plus{AC,#}(x8,s(plusAC(x,y)))
    plus{AC,#}(x8,plusAC(s(x),y)) -> plus{AC,#}(x,y)
    plus{AC,#}(x7,plusAC(0(),y)) -> plus{AC,#}(x7,y)
    plus{AC,#}(x6,plusAC(x,0())) -> plus{AC,#}(x6,x)
    plus{AC,#}(s(x),y) -> plus{AC,#}(x,y)
   Equations:
    plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
    plusAC(x3,x4) -> plusAC(x4,x3)
    timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
    timesAC(x3,x4) -> timesAC(x4,x3)
    plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
    plusAC(x4,x3) -> plusAC(x3,x4)
    timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
    timesAC(x4,x3) -> timesAC(x3,x4)
   TRS:
    plusAC(x,0()) -> x
    plusAC(0(),y) -> y
    plusAC(s(x),y) -> s(plusAC(x,y))
    timesAC(0(),y) -> 0()
    timesAC(s(0()),y) -> y
    timesAC(s(x),y) -> plusAC(y,timesAC(x,y))
    div(0(),y) -> 0()
    div(x,y) -> quot(x,y,y)
    quot(0(),s(y),z) -> 0()
    quot(s(x),s(y),z) -> quot(x,y,z)
    quot(x,0(),s(z)) -> s(div(x,s(z)))
    div(div(x,y),z) -> div(x,timesAC(y,z))
   S:
    plus{AC,#}(plusAC(x12,x13),x14) -> plus{AC,#}(x12,x13)
    plus{AC,#}(x12,plusAC(x13,x14)) -> plus{AC,#}(x13,x14)
    times{AC,#}(timesAC(x12,x13),x14) -> times{AC,#}(x12,x13)
    times{AC,#}(x12,timesAC(x13,x14)) -> times{AC,#}(x13,x14)
   AC-DP unlabeling:
    Equations#:
     plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
     plusAC(x3,x4) -> plusAC(x4,x3)
     timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
     timesAC(x3,x4) -> timesAC(x4,x3)
     plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
     plusAC(x4,x3) -> plusAC(x3,x4)
     timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
     timesAC(x4,x3) -> timesAC(x3,x4)
    DPs:
     plusAC(x8,plusAC(s(x),y)) -> plusAC(x8,s(plusAC(x,y)))
     plusAC(x8,plusAC(s(x),y)) -> plusAC(x,y)
     plusAC(x7,plusAC(0(),y)) -> plusAC(x7,y)
     plusAC(x6,plusAC(x,0())) -> plusAC(x6,x)
     plusAC(s(x),y) -> plusAC(x,y)
    Equations:
     plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
     plusAC(x3,x4) -> plusAC(x4,x3)
     timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
     timesAC(x3,x4) -> timesAC(x4,x3)
     plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
     plusAC(x4,x3) -> plusAC(x3,x4)
     timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
     timesAC(x4,x3) -> timesAC(x3,x4)
    TRS:
     plusAC(x,0()) -> x
     plusAC(0(),y) -> y
     plusAC(s(x),y) -> s(plusAC(x,y))
     timesAC(0(),y) -> 0()
     timesAC(s(0()),y) -> y
     timesAC(s(x),y) -> plusAC(y,timesAC(x,y))
     div(0(),y) -> 0()
     div(x,y) -> quot(x,y,y)
     quot(0(),s(y),z) -> 0()
     quot(s(x),s(y),z) -> quot(x,y,z)
     quot(x,0(),s(z)) -> s(div(x,s(z)))
     div(div(x,y),z) -> div(x,timesAC(y,z))
    S:
     plusAC(plusAC(x12,x13),x14) -> plusAC(x12,x13)
     plusAC(x12,plusAC(x13,x14)) -> plusAC(x13,x14)
     timesAC(timesAC(x12,x13),x14) -> timesAC(x12,x13)
     timesAC(x12,timesAC(x13,x14)) -> timesAC(x13,x14)
    Usable Rule Processor:
     Equations#:
      plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
      plusAC(x3,x4) -> plusAC(x4,x3)
      timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
      timesAC(x3,x4) -> timesAC(x4,x3)
      plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
      plusAC(x4,x3) -> plusAC(x3,x4)
      timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
      timesAC(x4,x3) -> timesAC(x3,x4)
     DPs:
      plusAC(x8,plusAC(s(x),y)) -> plusAC(x8,s(plusAC(x,y)))
      plusAC(x8,plusAC(s(x),y)) -> plusAC(x,y)
      plusAC(x7,plusAC(0(),y)) -> plusAC(x7,y)
      plusAC(x6,plusAC(x,0())) -> plusAC(x6,x)
      plusAC(s(x),y) -> plusAC(x,y)
     Equations:
      plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
      plusAC(x3,x4) -> plusAC(x4,x3)
      timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
      timesAC(x3,x4) -> timesAC(x4,x3)
      plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
      plusAC(x4,x3) -> plusAC(x3,x4)
      timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
      timesAC(x4,x3) -> timesAC(x3,x4)
     TRS:
      plusAC(0(),y) -> y
      plusAC(s(x),y) -> s(plusAC(x,y))
      plusAC(x,0()) -> x
     S:
      plusAC(plusAC(x12,x13),x14) -> plusAC(x12,x13)
      plusAC(x12,plusAC(x13,x14)) -> plusAC(x13,x14)
      timesAC(timesAC(x12,x13),x14) -> timesAC(x12,x13)
      timesAC(x12,timesAC(x13,x14)) -> timesAC(x13,x14)
     AC-RPO Processor:
      argument filtering:
       pi(plusAC) = [0,1]
       pi(timesAC) = [0,1]
       pi(0) = []
       pi(s) = []
      precedence:
       0 > plusAC > s > timesAC
      status:
       
      problem:
       Equations#:
        plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
        plusAC(x3,x4) -> plusAC(x4,x3)
        timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
        timesAC(x3,x4) -> timesAC(x4,x3)
        plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
        plusAC(x4,x3) -> plusAC(x3,x4)
        timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
        timesAC(x4,x3) -> timesAC(x3,x4)
       DPs:
        
       Equations:
        plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
        plusAC(x3,x4) -> plusAC(x4,x3)
        timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
        timesAC(x3,x4) -> timesAC(x4,x3)
        plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
        plusAC(x4,x3) -> plusAC(x3,x4)
        timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
        timesAC(x4,x3) -> timesAC(x3,x4)
       TRS:
        plusAC(0(),y) -> y
        plusAC(s(x),y) -> s(plusAC(x,y))
        plusAC(x,0()) -> x
       S:
        plusAC(plusAC(x12,x13),x14) -> plusAC(x12,x13)
        plusAC(x12,plusAC(x13,x14)) -> plusAC(x13,x14)
        timesAC(timesAC(x12,x13),x14) -> timesAC(x12,x13)
        timesAC(x12,timesAC(x13,x14)) -> timesAC(x13,x14)
      Qed